Robust feedstock selection system for the chemical process industries under market and operational uncertainty

1. A computer-implemented method for programming operations of a subject industrial plant based on feedstock selection planning, the method comprising: a) evaluating a first stage and a second stage at separate time intervals throughout a feedstock selection planning process of the subject industrial plant; b) determining, in the evaluation of the first stage, a set of robust feedstocks to procure on long-term contracts, wherein the determining includes: modeling feedstock procurement on long-term contracts as a first set of simulation cases of a non-linear model, wherein the first set of simulation cases includes a set of uncertain input parameters representing risks or uncertainties at a first time interval, including risk or uncertainties in operation conditions of the industrial plant; solving each simulation case of the first set of simulation cases, in parallel, to model different feedstock selection outcomes, wherein the modeled outcomes include optimal feedstocks, feedstock volumes, and operation conditions with respect to the given simulation case; and performing probabilistic analysis of the different modeled outcomes from the first set of simulation cases to determine the set of robust feedstocks to procure on long-term contracts; c) determining, in the evaluation of the second stage, a set of robust feedstocks to procure in a spot market, wherein the determining includes: modeling feedstock procurement in the spot market as a second set of simulation cases of the non-linear model, wherein the second set of simulation cases includes a set of uncertain input parameters representing uncertainty related to selecting feedstocks to procure in the spot market at a second time interval and further includes the determined set of robust feedstocks from the first stage; solving each simulation case of the second set of simulation cases to model different breakeven prices for one or more spot feedstocks; and performing probabilistic analysis on the different breakeven prices for each of the one or more spot feedstocks, wherein the performing determining which of the one or more spot feedstocks to procure in the spot market; d) determining optimal operating conditions to process the determined robust feedstocks from each stage in order to produce a set of products; and e) providing to a control system of the subject industrial plant the determined set of robust feedstocks and the optimal operating conditions to program the subject industrial plant operations.

2. The method of claim 1 , wherein the non-linear model is a mixed-integer, non-linear optimization problem (MINLP) model, and each simulation case comprises an independent instance of the MINLP model with a different set of realization values provided for the respective set of uncertain input parameters.

3. The method of claim 1 , wherein the simulation cases are generated by: (i) fitting a multivariate distribution to the uncertain input parameter data using kernel density estimation (KDE), or capturing correlations among the uncertain input parameters using a copula-based approach, and (ii) applying Monte-Carlo sampling to the respective multivariate distribution or the captured correlations.

4. The method of claim 1 , wherein the uncertain input parameters represent one or more of uncertain market conditions, uncertain operation conditions, and other uncertain industrial conditions.

5. The method of claim 1 , wherein performing probabilistic analysis of the different modeled outcomes further comprises: selecting robust feedstocks from the optimal feedstocks of the different modeled outcomes: generating a probabilistic feed slate distribution from the optimal feedstocks of the different modeled outcomes; and applying a threshold probability to the probabilistic feed slate distribution to select one or more robust feedstocks from the distributed feedstocks; and establishing an optimal feedstock volume for each selected robust feedstock by: generating a probabilistic distribution of feedstock volumes provided from the different modeled outcomes for the given robust feedstocks, and applying joint chance constraints derived from the probabilistic distribution of the feedstock volumes to establish optimal feedstock procurement volumes for the given robust feedstocks.

6. The method of claim 5 , wherein performing probabilistic analysis of the different modeled outcomes further comprises: generating a robust base case of the non-linear model, the robust base case being generated to include the joint chance constraints and a capacity-fulfillment constraint; and solving the generated robust base case, the solving determining the optimal procurement volumes corresponding to the set of robust feedstocks to procure on long-term contracts.

7. The method of claim 1 , wherein the determined robust feedstocks to procure on long-term contracts are validated by: comparing expected profits from the determined set of robust feedstocks from the first stage against expected profits from a deterministic approach.

8. The method of claim 1 , wherein solving each simulation case of the second set of simulation cases further comprises: for each simulation case of the second set of simulation cases: solving the given simulation case with the determined set of robust feedstocks from the first stage, the solving determining an optimal value of an objective function for the given simulation case; and for each spot feedstock of a set of available spot feedstocks: generating a feedstock case by forcing a fixed procurement volume of the given spot feedstock into the given simulation case, solving the feedstock case to determine an optimal value of an objective function for the given feedstock case, and calculating a breakeven price for the given spot feedstock based on: (i) the determined optimal objective function value for the given simulation case, and (ii) the determined optimal objective function value for the given feedstock case.

9. The method of claim 8 , wherein performing probabilistic analysis on the different breakeven prices for each spot feedstock of a set of available spot feedstocks, further comprises: generating ECDFs for breakeven analysis, each ECDF representing, for each spot feedstock, a correspondence between a calculated breakeven price and a risk level; and ranking each spot feedstock of the set of available spot feedstocks for breakeven analysis, the ranking determined by defining an incremental profit value between a market value and each calculated breakeven price for the given spot feedstock; and based on the ECDFs and the ranking, determining the set of robust feedstocks to procure in the spot market.

10. A computer system for programming operations of a subject industrial plant based on feedstock selection planning, the system comprising: one or more processors and associated memory, the one or more processors configured to evaluate a first stage and a second stage at separate time intervals throughout a feedstock selection planning process of the subject industrial plant, the one or more processors determining, in the evaluation of the first stage, a set of robust feedstocks to procure on long-term contracts, wherein the one or more processors comprise: a modeler engine configured to model feedstock procurement on long-term contracts as a first set of simulation cases of a non-linear model, wherein the first set of simulation cases includes a set of uncertain input parameters representing risks or uncertainties at a first time interval, including risk or uncertainties in operation conditions of the industrial plant; a solver engine configured to solve each simulation case of the first set of simulation cases, in parallel, to model different feedstock selection outcomes, wherein the modeled outcomes include optimal feedstocks, feedstock volumes, and operation conditions with respect to the given simulation case; and a solution analyzer configured to perform probabilistic analysis of the different modeled outcomes from the first set of simulation cases to determine the set of robust feedstocks to procure on long-term contracts; the one or more processors being further configured to determine, in evaluation of the second stage, a set of robust feedstocks to procure in the spot market, wherein: the modeler engine is configured to model feedstock procurement in a spot market as a second set of simulation cases of the non-linear model, wherein the second set of simulation cases includes a set of uncertain input parameters representing uncertainty related to selecting feedstocks to procure in the spot market at a second time interval and further includes the determined set of robust feedstocks from the first stage; the solver engine is configured to solve each simulation case of the second set of simulation cases to model different breakeven prices for one or more spot feedstocks; and the solution analyzer is configured to perform probabilistic analysis on the different breakeven prices for each of the one or more spot feedstocks, wherein the performing determining which of the one or more spot feedstocks to procure in the spot market; and the one or more processors being further configured to determine optimal operating conditions to process the determined robust feedstocks from each stage in order to produce a set of products; the solution analyzer providing to a control system of the subject industrial plant the determined set of robust feedstocks and the optimal operating conditions to program the subject industrial plant operations.

11. The system of claim 10 , wherein the non-linear model is a mixed-integer, non-linear optimization problem (MINLP) model, and each simulation case comprises an independent instance of the MINLP model with a different set of realization values provided for the respective set of uncertain input parameters.

12. The system of claim 10 , wherein the modeler engine is further configured to generate the simulation cases by: (i) fitting a multivariate distribution to the uncertain input parameter data using kernel density estimation (KDE), or capturing correlations among the uncertain input parameters using a copula-based approach, and (ii) applying Monte-Carlo sampling to the respective multivariate distribution or the captured correlations.

13. The system of claim 10 , wherein the uncertain input parameters represent one or more of uncertain market conditions, uncertain operation conditions, and other uncertain industrial conditions.

14. The system of claim 10 , wherein the solution analyzer is further configured to: select robust feedstocks from the optimal feedstocks of the different modeled outcomes by: generating a probabilistic feed slate distribution from the optimal feedstocks of the different modeled outcomes; and applying a threshold probability to the probabilistic feed slate distribution to select one or more robust feedstocks from the distributed feedstocks; and establish an optimal feedstock volume for each selected robust feedstock by: generating a probabilistic distribution of feedstock volumes provided from the different modeled outcomes for the given robust feedstocks, and applying joint chance constraints derived from the probabilistic distribution of the feedstock volumes to establish optimal feedstock procurement volumes for the given robust feedstocks.

15. The system of claim 14 , wherein the solution analyzer is further configured to: generate a robust base case of the non-linear model, the robust base case being generated to include the joint chance constraints and a capacity-fulfillment constraint; and solve the generated robust base case, the solving determining the optimal procurement volumes corresponding to the set of robust feedstocks to procure on long-term contracts.

16. The system of claim 10 , wherein the one or more processors are further configured to validate the determined robust feedstocks to procure on long-term contracts by: comparing expected profits from the determined set of robust feedstocks from the first stage against expected profits from a deterministic approach.

17. The system of claim 10 , wherein the solver engine is further configured to: for each simulation case of the second set of simulation cases: solve the given simulation case with the determined set of robust feedstocks from the first stage, the solving determining an optimal value of an objective function for the given simulation case; and for each spot feedstock of a set of available spot feedstocks: generate a feedstock case by forcing a fixed procurement volume of the given spot feedstock into the given simulation case, solve the feedstock case to determine an optimal value of an objective function for the given feedstock case, and calculate a breakeven price for the given spot feedstock based on: (i) the determined optimal objective function value for the given simulation case, and (ii) the determined optimal objective function value for the given feedstock case.

18. The system of claim 17 , wherein the solution analyzer is further configured to: generate ECDFs for breakeven analysis, each ECDF representing, for each spot feedstock, a correspondence between a calculated breakeven price and a risk level; and rank each spot feedstock of the set of available spot feedstocks for breakeven analysis, the ranking determined by defining an incremental profit value between a market value and each calculated breakeven price for the given spot feedstock; and based on the ECDFs and the ranking, determine the set of robust feedstocks to procure in the spot market.

19. The method of claim 1 , wherein programming of operations includes programming any of a plant system application, a blending control system, a process control system, and other control systems.